The current outbreak of the coronavirus disease 2019 (COVID-19) is an unprecedented example of how fast an infectious disease can spread around the globe (especially in urban areas) and the enormous impact it causes on public health and socioeconomic activities. Despite the recent surge of investigations about different aspects of the COVID-19 pandemic, we still know little about the effects of city size on the propagation of this disease in urban areas. Here we investigate how the number of cases and deaths by COVID-19 scale with the population of Brazilian cities. Our results indicate small towns are proportionally more affected by COVID-19 during the initial spread of the disease, such that the cumulative numbers of cases and deaths per capita initially decrease with population size. However, during the long-term course of the pandemic, this urban advantage vanishes and large cities start to exhibit higher incidence of cases and deaths, such that every 1% rise in population is associated with a 0.14% increase in the number of fatalities per capita after about four months since the first two daily deaths. We argue that these patterns may be related to the existence of proportionally more health infrastructure in the largest cities and a lower proportion of older adults in large urban areas. We also find the initial growth rate of cases and deaths to be higher in large cities; however, these growth rates tend to decrease in large cities and to increase in small ones over time.

We investigated daily COVID-19 cases and deaths in the 337 lower tier local authority regions in England and Wales to better understand how the disease propagated over a 15-month period. Population density scaling models revealed residual variance and skewness to be sensitive indicators of the dynamics of propagation. Lockdowns and schools reopening coincided with increased variance indicative of conditions with local impact and country scale heterogeneity. University reopening and December holidays reduced variance indicative of country scale homogenisation which reached a minimum in mid-January 2021. Homogeneous propagation was associated with better correspondence with normally distributed residuals while heterogeneous propagation was more consistent with skewed models. Skewness varied from strongly negative to strongly positive revealing an unappreciated feature of community propagation. Hot spots and super-spreading events are well understood descriptors of regional disease dynamics that would be expected to be associated with positively skewed distributions. Positively skewed behaviour was observed; however, negative skewness indicative of “cold-spots” and “super-isolation” dominated for approximately 8 months during the period of study. In contrast, death metrics showed near constant behaviour in scaling, variance, and skewness metrics over the full period with rural regions preferentially affected, an observation consistent with regional age demographics in England and Wales. Regional positions relative to density scaling laws were remarkably persistent after the first 5–9 days of the available data set. The determinants of this persistent behaviour probably precede the pandemic and remain unchanged.

The urban scaling hypothesis has improved our understanding of cities; however, rural areas have been neglected. We investigated rural–urban population density scaling in England and Wales using 67 indicators of crime, mortality, property, and age. Most indicators exhibited segmented scaling about a median critical density of 27 people per hectare. Above the critical density, urban regions preferentially attract young adults (25–40 years) and lose older people (> 45 years). Density scale adjusted metrics (DSAMs) were analysed using hierarchical clustering, networks, and self-organizing maps (SOMs) revealing regional differences and an inverse relationship between excess value of property transactions and a range of preventable mortality (e.g. diabetes, suicide, lung cancer). The most striking finding is that age demographics break the expected self-similarity underlying the urban scaling hypothesis. Urban dynamism is fuelled by preferential attraction of young adults and not a fundamental property of total urban population.

We investigated daily COVID-19 cases and death in the 337 lower tier local authority regions in England and Wales to better understand how the disease propagated over a 10-month period. Population density scaling models revealed residual variance and skewness to be sensitive indicators of the dynamics of propagation. Lockdowns and schools reopening triggered increased variance indicative of outbreaks with local impact and country scale heterogeneity. University reopening and December holidays triggered reduced variance indicative of country scale homogenisation which reached a minimum after New Year. Homogeneous propagation was associated with better correspondence with normally distributed residuals while heterogeneous propagation was more consistent with skewed models. Skewness varied from strongly negative to strongly positive revealing an unappreciated feature of community propagation. Hot spots and super-spreading events are well understood descriptors of regional disease dynamics that would be expected to be associated with positively skewed distributions. Positively skewed behaviour was observed; however, negative skewness indicative of “cold-spots” and “super-isolation” dominated for approximately 4 months during the period of study. In contrast, death metrics showed near constant behaviour in scaling, variance, and skewness metrics over the full period with rural regions preferentially affected, an observation consistent with regional age demographics in England and Wales.